Physics Question #1283

The answer

We actually don't know whether the quark or neutrino have a "size" in the conventional sense. The sizes of elementary particles are defined by the regions of space that they occupy, something that we can directly measure by colliding particles together and seeing how they ricochet off each other. This is analogous to how Lord Rutherford discovered the nucleus of the atom by firing alpha particles at gold atoms.

In the case of quarks and electrons, studies of very high-energy collisions of electrons and protons tell us that the sizes of these objects are less than about 10^{-18} m. That is 0.0000000000000000001m. We can't do similar experiments on neutrinos, but we've assumed that they behave just like electrons.

Both types of particles have mass, and here the quarks win out, though the actual value of that mass depends on how it's defined, given that we haven't observed individual quarks. The quarks come bound up in pairs or triplets and the mass they appear to have depends on how we model that bound state. The up and down quarks have masses of around a few MeV/c^2 (a strange unit for mass -- it's a million electron-volts divided by the speed of light squared -- 1 MeV/c^2 = 1.8 x 10^(-24) kg), while the heaviest quark, the top quark, has a mass of around 172,000 MeV/c^2. In the case of neutrinos, we only have rough constraints on their masses, which we get by looking at how neutrinos are produced when nuclei decay and how often one type of neutrino changes into another type (or flavour). We believe that neutrino masses are less than about 1 eV/c^2, or at least a million times lighter than quarks.

The neutrino wins by a long shot. It takes three quarks to make up a proton or neutron (the building blocks of the elements), so each quark has a mass roughly one-third that of a proton or neutron (each of these, in turn, weighs about two millionths of a billionth of a billionth of a gram!). The mass (or equivalently, rest energy) of a neutrino is still being worked out but we know the heaviest type of neutrino weighs at least 30 times less than a proton or neutron (or at least 10 times smaller than a quark). The lightest type of neutrino weighs at least several hundred million times less than a proton or neutron.

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